A100175 Structured triakis tetrahedral numbers (vertex structure 4).

1, 8, 30, 76, 155, 276, 448, 680, 981, 1360, 1826, 2388, 3055, 3836, 4740, 5776, 6953, 8280, 9766, 11420, 13251, 15268, 17480, 19896, 22525, 25376, 28458, 31780, 35351, 39180, 43276, 47648, 52305, 57256, 62510, 68076, 73963, 80180, 86736, 93640, 100901, 108528

Offset: 1

Author

James A. Record (james.record(AT)gmail.com), Nov 07 2004

Keywords

• easy
• nonn

Comments

Equals binomial transform of [1, 7, 15, 9, 0, 0, 0, ...] where (1, 7, 15, 9) = row 3 of triangle A038763. - Gary W. Adamson, Jul 19 2008

Equals convolution square of 1, 4, 7, 10, 13, 16, 19, ..., A016777. - Gary W. Adamson, Jul 28 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000578 (alternate vertex), A100145 for more on structured numbers.

Cf. A038763.

Programs

Magma

[(3*n^3-3*n^2+2*n)/2: n in [1..50] ]; // Vincenzo Librandi, Aug 02 2011

Mathematica

CoefficientList[Series[x (2x+1)^2/((x-1)^4),{x,0,50}],x] (* or *) LinearRecurrence[{4,-6,4,-1},{0,1,8,30},50] (* Harvey P. Dale, Mar 18 2023 *)

Formula

a(n) = (3*n^3 - 3*n^2 + 2*n)/2.

G.f.: x*(2*x+1)^2 / ( (x-1)^4 ).